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The graph of the velocity function of a particle is shown in the figure. Sketch the graph of a position function.
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Calculus 1 / AB
Calculus 2 / BC
Applications of Differentiation
Missouri State University
Oregon State University
University of Michigan - Ann Arbor
In mathematics, the volume of a solid object is the amount of three-dimensional space enclosed by the boundaries of the object. The volume of a solid of revolution (such as a sphere or cylinder) is calculated by multiplying the area of the base by the height of the solid.
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The graph of the velocity …
(a) A particle starts by m…
The position vector for a …
The displacement-time grap…
The graph of the position …
Yeah, so first problem, we see that the from 0 to 1 we're going to be positive and uh increasing, so we'll zoom in here a little closer to get a good view on the graph. Um So what this is gonna look like is we're going to be positive and increasing from 0 to 1 and then it's going to be from 1 to 2 positive and constant. So like this like a straight line then from 2 to 3 it's going to be positive and decreasing, so it's going to be concave down like this, then from 3 to 4, it's going to be zero in constant. So I have something like this from 4 to 5, it will be negative and decreasing, and then from uh 45 that's gonna be decreasing at a pretty high rate, so we'll have that going a little deeper. Mhm. And then for six to infinity it's going to be zero and constant. From 5 to 6, it's gonna be negative and decreasing, but at a very low rate. So like this, and then from six to infinity, you can use your own concepts. We're just going to draw that line Zero. This is going to be our final graph.
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